Method and apparatus for measuring surface configuration

ABSTRACT

A method of measuring the surface configuration of a liquid surface, e.g. to measure surface tension. Liquid samples are confined in wells, e.g. of a multi-well microtitle plate, and a light beam is passed through the sample offset from the centre of the well. The intensity of the reflected or transmitted light beam is dependent upon the angle of incidence with the liquid surface, which varies with changes in surface tension of the liquid. Thus measurement of the reflected or transmitted intensity can be used as a measurement of the surface tension The method can also be used to measure viscosity by agitating the sample and measuring the rate of change of curvature of the sample surface during or after agitation. The method is also applicable to measuring surfaces other than liquids, e.g. of a membrane being deformed under pressure where, again the angle of incidence of a light beam on the membrane varies with deformation of the membrane.

[0001] The present invention relates to a method and apparatus formeasuring the configuration of a surface, in particular the surface of aliquid-liquid or liquid-gas interface, but also other surfaces, such asmembranes. In its application to measuring liquid-liquid, liquid-gasinterfaces it is useful in measuring various properties of liquids, suchas surface tension.

[0002] There are a variety of traditional methods of measuring thesurface tension of liquids, such as the Wilhelmy Plate device, the DeNouy Ring method, capillary rise methods, the Jaeger bubble pressureapproach and techniques based on thin films if the liquid will film inair. However, although accurate, these methods are rather difficult toset up and are not suited to repeated, quick measurements on differentsamples. Further these methods require many millilitres of sample liquidand take several minutes per sample.

[0003] The configuration of the surface of a liquid contained, forinstance, in a well is dependent inter alia upon the surface tension ofthe liquid and the contact angle between the liquid and the well and GB1 447 262 discloses a contactless method for measuring surface tensionbased on this. In this method the curvature of the meniscus of a liquidis a measured by reflecting light beams off two spaced points on themeniscus and measuring the different angles at which the light beam isreflected. A knowledge of the separation of the two points, and of theangles of reflection can be used in a geometrical formula to calculatethe surface tension of the liquid. The instrument however relies onprecise optics, and also on the movement of a detector to measure thedifferent angles of reflection. This makes the instrument rather complexand, again, difficult to set up, and also makes the instrumentunsuitable for repeated, quick measurements of a multiplicity ofsamples.

[0004] The present invention provides a method of measuring theconfiguration of a surface which does not rely on contacting thesurface, yet which is reliable, repeatable and quick both to set-up andin use. When it is used to measure the configuration of a liquidsurface, it provides a particularly easy way of measuring the surfacetension of that liquid.

[0005] According to the present invention there is provided a method ofmeasuring the configuration of a surface comprising illuminating thesurface with a beam of light and measuring the intensity of thereflected or transmitted beam.

[0006] The intensity of the transmitted, or reflected, light beam varieswith the angle of incidence and the effect of changing the configurationof a surface, e.g. by changing the curvature through a chance in surfacetension, is to change the angle of incidence at some points, someasuring the intensity of the transmitted or reflected light gives ameasure of the configuration. Where the configuration of the surface isdependent upon, e.g. the concentration or nature of the liquid, themeasurements are indicative of that concentration or nature. Further,the method is contactless and nondestructive.

[0007] The surface may be the meniscus of a liquid contained in, say, awell in a plate, in which case the measurement is dependent upon and canbe converted into a measure of the surface tension of the liquid. Infact there is a relationship, the Young and LaPlace equation, betweenthe three pair-wise interactions (solid-liquid, solid-vapour andliquid-vapour), where the solid is the material of the plate, whichrelates the surface tensions and the contact angle (θ) such that:

Υ_(sv)=Υ_(sl)+Υ_(lv) Cos θ

[0008] In this case, the first term is solid-vapour and will be constantfor a given plate material whatever the liquid, the second term is thesolid-liquid wettability that will depend on the material of the plateand the liquid, while the third term is the true surface tension, whosecontribution is modified by the contact angle. Given this interactionthe surface tension may most conveniently be calculated from theintensity measurement by using a look-up table based on calibrationusing data relating the surface tension (e.g. published data ormeasurements using a traditional technique) to the composition of theliquid (e.g. surfactant concentration). In some circumstances it ispossible to use the values of the reflected or transmitted intensity ina formula relating them to the angle of incidence, and thus thecurvature, and in turn the surface tension.

[0009] The method works with small quantities of liquid, as low as 100microlitres or 50 microlitres, e.g. when the liquid is in the wells of a96 well assay plate.

[0010] A plurality of measurements may be made, optionallysimultaneously, at points spaced across the surface. The method mayfurther comprise calculating the ratio of the intensities of thetransmitted or reflected beams at two of said plurality of points, thesize of the ratio indicating the degree of curvature of the meniscus.

[0011] The surface may be the surface of one of a plurality of samples,eg liquid samples on a multi-well assay plate, and the step of measuringthe intensity comprises measuring the intensity for each of saidsamples. In this case the beam of light is preferably incident upon thesurface of the liquid offset from the centre of the well.

[0012] The method is fast compared to traditional methods of measuringsurface tension. In one embodiment measurements on all the wells of a 96well assay plate can be completed within 30 seconds, giving a time persample of just over 300 msec for sequential reading.

[0013] The method may be used to measure the surface activity of ananalyte in a liquid by making intensity measurements for a plurality ofdifferent analyte concentrations. This can be obtained as a readout ofan assay where the product is surface active

[0014] The method may also be used to correct photometry measurementsmade by a plate reader on a plurality of samples contained in respectivewells of a microtitre plate for errors caused by variations in relativeposition of the well and the light beam of the reader. In this case themethod comprises the steps of illuminating each sample with a light beamof a frequency to which the samples should have uniform response,measuring the intensity of the transmitted or reflected light, andderiving therefrom a correction factor for the variation from well towell of the intensity caused by variation in the angle of incidence ofthe light beam on the surface. The photometry measurements can then becorrected using the correction factors. If a standard set ofconcentrations of a known surface active component is present in theassay, correction factors may be derived for only some wells ofthe-plate and be interpolated for other wells of the plate.

[0015] The speed of the method also makes it suitable for screening allwells of an assay for unexpected surface active compounds duringhigh-throughput screening of large libraries of compounds in anyphotometric assay (during any photometry where there may be unexpectedsurface effects).

[0016] The method may also be used to measure the viscosity of a liquidby agitating the liquid to deform the surface, and measuring the changein the configuration of the surface, eg the rate at which the surfacereturns to its stationary equilibrium position after ceasing theagitation. The agitation may be adapted to create a vortex in theliquid.

[0017] Another aspect of the invention provides apparatus for carryingout the method on a liquid sample supported on a substrate. Theapparatus comprises a light source for producing a light beam forilluminating the liquid surface at a fixed angle and adapted toilluminate the sample at a predetermined offset from the sample centreand means for measuring the intensity of the transmitted or reflectedlight.

[0018] The substrate may comprise a well containing the sample, thelight beam being parallel to the walls of the well and at saidpredetermined offset from the centre of the well.

[0019] An alternative method and technique provide a method of measuringthe deformation of a membrane, e.g. as a result of pressure on thesurface of the membrane, by illuminating the membrane and measuring thevariation in transmitted or reflected light as the membrane deformschanging the angle of incidence of the light on the membrane. This isparticularly useful for measuring osmotic pressure. The membrane canarranged to close a chamber into which liquid passes by osmosis throughthe membrane, in which case it has to be semi-permeable, or by osmosisthrough a different route.

[0020] The invention will be further described by way of non-limitativeexample, with reference to the accompanying drawings in which:

[0021]FIG. 1 is a schematic view of a first embodiment of the invention;

[0022]FIG. 2 is a diagram illustrating the principles of the invention;

[0023]FIG. 3 is a schematic diagram illustrating an alternative use ofthe invention;

[0024]FIG. 4 is a graph showing experimental results from the firstembodiment of the invention;

[0025]FIG. 5 is a schematic diagram showing another use of theinvention;

[0026] FIGS. 6(A) to (F) are graphs showing further experimental resultswith the first embodiment of the invention;

[0027] FIGS. 7(A) to (C) show further experimental results with thefirst embodiment of the invention; and

[0028]FIG. 8(A) to (C) show a comparison between surface tensionmeasured by the method of the invention and measured by a conventionalmethod.

[0029]FIG. 1 illustrates systematically an arrangement in which liquidsamples are contained in wells 1 of a microtitre plate 3. The wells canbe placed successively under detection head 5, either by movement of theplate 3, or movement of the detection head 5 in X and Y directions asshown. The microtitre plate 3 is supported on a substrate 115 whoseposition and movement are controlled by a stage controller 17. Thedetection head 5 transmits a light beam 7 through the wells to adetector 9. The detector 9 measures the intensity of the transmittedlight beam and the intensity measurements are stored in a store 11processed by a processor 19 and displayed on a display 21. Theillumination is controlled by a light controller 13.

[0030] It will be appreciated that in practice the plate 3 can be amulti-well (e.g. 96 well) plate of the normal experimental type, on acommercially available support 15. This support 15 and controller 17 mayinclude temperature control for the plate. The illumination anddetection can conveniently by means of an adapted microtitre platereader. In this embodiment the light source is a filtered Xenon flashlamp which provides a light beam 0.25 millimetres in diameter. In atypical 96 well plate made of polystyrene the wells are 6 millimetres indiameter. A laser light source such as a laser diode could be used asthe light source.

[0031] The principles of the invention are illustrated in FIG. 2. Asample of liquid 2 can be seen occupying the wells 1. The surface 2A ofthe liquid extends from one side of the well to the other. Depending onthe liquid, and the material of the well the liquid may not meet thesides of the well at 90 degrees but be in the form of a curve (ameniscus) extending from one side of the well to the other. Inpolystyrene assay plates a sample of water has a perfectly flat surface(i.e. it does meet the sides at 90°). A meniscus only appears with theaddition of surface active substances to the water. For an infinitelythin light beam precisely aligned with the geometrical centre of thewell, as illustrated at 1 in FIG. 2, the incident light beam 11 will beat normal incidence on the surface of the liquid. Most of the light willbe transmitted in a light beam T1, while a small proportion will bereflected in the normally reflected light beam R1. However, if the lightbeam is displaced from the centre of the well, as at 2, the incidentlight beam 12 is incident at an angle of θ1 on the surface. The effectof this is that the reflected light beam R2 will be more intense thanthe reflected light beam R1, and the transmitted light beam T2 will beless intense than the transmitted light beam T1. Thus the measurement ofthe intensity of either the transmitted or reflected light beam isindicative of the angle of incidence on the liquid surface and, as theincident light beam is in fixed relation to the well, i.e. parallel tothe well sides, this in turn is indicative of the angle of the liquidsurface. The angle of the liquid surface is dependent upon the surfacetension (as given by the Young and LaPlace equation). As the surfacetension decreases, the curvature increases for aqueous solutions inpolystyrene.

[0032] This effect can be seen in the results shown in FIG. 4. Toproduce FIG. 4 a variety of samples consisting of aqueous solutions ofthe non-ionic detergent Triton X-100 at different concentrations wereloaded into a 96 well microtitre plate. A conventional microtitre platereader was modified so that the optical density of each sample wasmeasured at a position offset by 2.4 millimetres from the centre of thewell. In FIG. 4 the logarithm of the apparent optical density at awavelength of 450 nanometres is plotted vertically and the logarithm ofthe percentage concentration of detergent is plotted horizontally. Itcan be seen that as the concentration of detergent decreases, and thusthe surface tension of the liquid sample increases (resulting in adecrease in curvature) the apparent optical density (obtained bymeasuring the intensity of the transmitted beam) also decreases. This isbecause the decreasing angle of incidence means that the transmittedbeam becomes more intense and the reflected beam less intense. FIG. 4demonstrates that this method is capable of detecting changes inconcentration as low as 1 ppm. This is approximately two orders ofmagnitude more sensitive than an estimation based on droplet weight.

[0033] FIGS. 6(A) to (F) show the results of measurements similar tothose depicted in FIG. 4 but made using different polystyrene 96 wellplates. FIG. 6(A) uses a Labsystems Cliniplate which is uncharged. FIG.6(B) uses a Greiner plate which has an intermediate charge and FIG. 6(C)uses a Costar EIA.RIA plate which is highly charged to allow attachmentof proteins for adsorption assays. As can be seen all of the curves showa linear region which represents dependence of the intensity measurementon concentration and thus on surface tension and contact angle. FIGS.6(D) to (F) show corresponding measurements for a different detergentSDS on respectively the CLINIPLATE, Greiner microclear and CostarEIA/RIA assay plates.

[0034] Although FIGS. 4 and 6 show the results of making a measurementat only one point on the sample surface, in an alternative embodimentmeasurements were made at six different offsets spaced by 0.5 mm. This,therefore, gives an accurate reading of the curvature of the surface.The surface tension can be calculated either by use of a geometricalformula, or by use of a look-up table. This can most conveniently becreated by calibrating the apparatus using samples of known surfacetension (measured by one of the traditional methods).

[0035] FIGS. 7(A) to 7(C) illustrate the relationship between the lighttransmission (plotted vertically) and the surface tension (plotted onthe horizontal axis) for six different concentrations of C10E8, anon-ionic surfactant with the formula CH₃ (CH₂)₉—(O—CH₂—CH₂)₈—OH on thesame three different types of assay plate. The concentration isconverted into a surface tension value using published data (based onmeasurements by the bubble diameter method—which is one of thetraditional methods) and the light transmission is measured using theapparatus of FIG. 1 for each concentration for each of the three typesof assay plate. FIG. 7(A) is for the Greiner plate, FIG. 7(B) is for theLabsystems Cliniplate and FIG. 7(C) is for the Costar plate. A leastsquares regression analysis resulting in a linear fit to the data isalso illustrated on each graph. For each regression point the predictedsurface tension and absorbance are plotted as the “predicted readings”.Thus this linear fit (or any other fit if appropriate) can be usedeffectively as a look-up table allowing a light transmission measurementmade by the invention to be converted in one step into a surface tensionvalue, or into a concentration value.

[0036] FIGS. 8(A), (B) and (C) compare the method of this embodiment ofthe invention with a conventional method for surface tension measurement(the De Nouy ring method) on a dilution series of C10E8 as used toproduce FIGS. 7(A)-(C). The figures show the regression line fit betweenmeasured surface tension and the absorption of light of wavelength 450nanometres at 2.4 mm offset from the centre of the well on a 96 wellplate. It will be seen that the agreement between the two methods isvery good, the correlation coefficient for the Greiner plate, forexample, is 0.96. In addition, for both the Greiner plate and theLabsystems plate the only widely divergent point is that at the lowestconcentration of detergent. Here, the value obtained in the De Nouy ringassay is the one to deviate from the linear fit, while the method of theinvention gives a value close to the predicted value.

[0037] To improve the speed of measurement the apparatus can be adaptedso that multiple measurements are made simultaneously within each wellusing multi-channel optics. In other words, the light source 5 isadapted to produce multiple light beams which are simultaneouslydetected. Alternatively rather than exact simultaneity, the light beamscan be produced in succession, so that only a single broad detector 9needs to be used.

[0038] The apparatus can also be adapted to measure all of the wells inthe plate 3 simultaneously, using a larger scale multi-channel opticalreader. In this case a light source 7 and detector 9 are provided foreach of the wells 3. With these adaptations an entire 96 well plate canbe measured several times a second, or a row or column of wells or anindividual well can be measured several hundred times a second.

[0039] It will also be appreciated that the assay plate can be handledremotely using conventional equipment and the plates can be sealedbefore being passed to the reader for measurement. This means that it ispossible to use the system to make measurements on extremely toxic orinfectious liquids. Further, measurements can be made in a non-airatmosphere (e.g. under argon to avoid oxidative damage); to measure inthe presence of highly volatile compounds, or to measure at a pressureabove or below atmospheric.

[0040] The stage controller 17 may also be adapted to control thetemperature of the assay plate. This means that the surfaceconfiguration can be measured at a range of defined temperatures andcan, for instance, allow repeated measurements to be made during arising and falling temperature ramp. This can usefully give aquantification of temperature related surface effects such as surfacetension hysteresis. Furthermore, the speed and repeatability ofmeasurement allows measurements to be repeated during a reaction, forinstance to follow surface tension changes following initiation of areaction by reagent addition optionally within the reader. Thus the factthat the measurements are contactless and nondestructive and repeatablemakes the apparatus highly versatile.

[0041] One application of the invention is in the field of processcontrol where it is desired to maintain a consistent product quality asmeasurable by surface activity, such as surface tension. In thisembodiment the apparatus is adapted to take regular samples of theproduct and subject them to measurement. It is only necessary to makeone measurement, i.e. at one position on the surface of the sample, asone is only interested in determining whether the quality of the productis changing, rather than in finding absolute values. Thus a singlemeasurement at an offset (for instance at position 2 in FIG. 2) wouldsuffice. The result can be fed back to the production process to controla process parameter, for instance, the proportion of some reagents.

[0042] It will be appreciated that where a plurality of measurements aremade across the surface the rate of change across the surface of theintensity of the transmitted or reflected beam may be of interest. Anindication of this rate of change can be obtained by determining theratio of intensities measured at two different points. The effect of thecurvature on the intensity is greatest offset from the centre and thusthis is the preferred location for measurement (either when single ormultiple measurements are being made), but because the light beams inuse are not infinitely thin (but have a finite diameter), even at thecentre of the well the intensity of the transmitted or reflected beam isaffected by the curvature of the surface. Thus it is possible to makemeasurements even at the centre of the well.

[0043] A similar application of the invention lies in the determinationof surface activity of an analyte in a liquid. The change in surfaceactivity with concentration (or with time in the case of a reaction) canbe evaluated by measuring the curvature of the surface of the liquid asdescribed above.

[0044] It will be appreciated that the effect of the curvature of thesurface of samples in a microtitre plate can be a cause of significanterrors in the course of normal photometry measurements. Thus influorescence or colorimetry measurements on samples in microtitreplates, unexpected variations can occur if the light source and detectorhead are not consistently aligned with the sample well or in thepresence of compounds with unexpected surfactant properties. It is foundthat typically the alignment between the light beam and the well variesprogressively as the measurements progress across the plate. The presentinvention provides a way of correcting for such errors because it allowsa determination of the variation in intensity of the transmitted orreflected light beam caused by this misalignment, and this variation canthen be subtracted from the actual photometry measurement. In oneembodiment this is achieved by first making measurements on the samplesat a light frequency to which the sample material itself respondsuniformly (e.g. does not fluoresce or absorb the light) i.e. such thatthe only variation between samples is caused by any defectivecentralisation of the light beam. These variations are measured for thesamples and then correction factors are calculated. These correctionfactors are used to correct the photometry measurements which are madeat a frequency to which the samples respond, e.g. fluoresce, independence upon the concentration of analyte therein. Where thedefective centralisation is progressive across the plate, correctionfactors can be measured for only a few of the sample wells, and theninterpolated for the rest of them. It may be that for one reader, or onerun, the correction factors only need to be calculated once as thealignment errors are the same every time. Such correction allows theavoidance of false results created by beam offsets, especiallyimportantly a reduction in false negatives, when screening a largelibrary of incompletely characterised compounds using any photometricscreening assay in multiwell plates.

[0045] In the embodiments above the invention has been used to measuresurface tension. However the measurements made are characteristic of theangle of incidence of the light beam on the surface and thus theinvention is applicable to the measurement of other quantities affectingthe surface. One example of this is illustrated in FIG. 3 in a methodfor measuring the viscosity of samples. As schematically illustrated inFIG. 3 the stage controller 17 is programmed to agitate the sample, inthis case to swirl them, to create a vortex in each sample well. Theresult of this vortex is that the liquid is forced towards the outsideof the well, and thus the surface curvature increases from the restposition shown dotted at 2 a, to the position shown at 2 b. Theagitation can then be ceased and the rate at which the surface returnsto the rest position 2 a is dependent upon the viscosity of the sample.This rate of change is measured in exactly the same way as in theembodiments above, i.e. by use of a light beam at position 2 in FIG. 2(i.e. offset from the centre of the well). Alternatively, rather thanmeasuring the relaxation time, it is possible simple to measure thechange in the curvature created by the agitation which, again, will bedependent upon the viscosity of the liquid.

[0046] Another alternative application is illustrated in FIG. 5. In FIG.5 two samples 2 c and 2 d of different concentrations are separated by asemi-permeable membrane 50. Over the course of time, solvent will betransferred by osmosis across the membrane from the less concentratedsample to the more concentrated sample (illustrated in FIG. 5 as beingfrom sample 2 c to 2 d). This will increase the amount of liquid underthe semi-permeable membrane 50 causing it to deform over time. Themeasurement light beam, which can be offset from the centre (as atposition 2 in FIG. 2), will be incident on the semi-permeable membrane50 at an angle of incidence which varies with time as the membranedeforms. This variation will cause a variation in the intensity of thetransmitted or reflected beam, measurable just as in the embodimentsdescribed above. It will, of course, be appreciated that thesemi-permeable membrane needs to be non-opaque. Further, although FIG. 5illustrates the osmosis as occurring across the semi-permeable membrane50, the membrane 50 can be arranged to be impermeable, though flexible,if a different path for osmosis is provided. Thus the osmosis need notnecessarily occur across the membrane whose deformation is beingmeasured. Further, the variation in pressure beneath the membrane neednot necessarily be created by osmosis, but could be created by any othertransport mechanism, the membrane 50 simply being used as a convenientway of measuring the change in the pressure of the liquid or gas beneathit.

[0047] In the embodiments discussed above it is the transmitted lightbeam which is measured. However, the intensity of the reflected lightbeam varies with the change of angle of incidence and thus is it isequally possible to use the reflected light beam for measurement.

1. A method of measuring the configuration of a surface comprisingilluminating the surface with a beam of light and measuring theintensity of the reflected or transmitted beam.
 2. A method according toclaim 1 wherein a plurality of measurements are made at points spacedacross the surface.
 3. A method according to claim 2 wherein saidplurality of measurements are made simultaneously.
 4. A method accordingto claim 2 or 3 further comprising calculating the ratio of theintensities of the transmitted or reflected beams at two of saidplurality of points.
 5. A method according to any one of the precedingclaims wherein the surface is the surface of one of a plurality ofsamples, and the step of measuring the intensity comprises measuring theintensity for each of said samples.
 6. A method according to any one ofthe preceding claims wherein the surface is a meniscus of a liquid.
 7. Amethod according to claim 6 wherein the sample is contained in a well,and the surface extends between the walls of the well.
 8. A methodaccording to claim 7 wherein the beam of light is incident upon thesurface of the liquid offset from the centre of the well.
 9. A methodaccording to claim 6 or 7 wherein the well is one of an array of wells.10. A method according to claim 9 comprising simultaneously illuminatingthe liquid surface in each of the wells and measuring the transmitted orreflected intensity.
 11. A method according to any one of claims 6 to 10further comprising the step of determining from the intensity of thetransmitted or reflected beam the surface tension of the liquid.
 12. Amethod of measuring the surface activity of an analyte in a liquid bymeasuring the configuration of the surface of the liquid by the methodof any one of the preceding claims for a plurality of different analyteconcentrations.
 13. A method of correcting photometry measurements madeby a plate reader on a plurality of samples contained in respectivewells of a microtitre plate for errors caused by variations in therelative position of the wells and the light beam of the reader, themethod comprising the steps of illuminating each sample with a lightbeam of a frequency to which the samples have uniform response,measuring the intensity of the transmitted or reflected light, andderiving therefrom a correction factor for the variation from well towell of the intensity caused by variation in the angle of incidence ofthe light beam on the surface, and correcting said photometrymeasurements using said correction factors.
 14. A method according toclaim 13 wherein correction factors are derived for only some wells ofthe plate and are interpolated for other wells of the plate.
 15. Amethod of measuring the viscosity of a liquid by agitating the liquid todeform the surface, and measuring the change in the configuration of thesurface using the method of any one of claims 1 to
 10. 16. A methodaccording to claim 15 comprising the step of ceasing the agitation andmeasuring the rate of change of the configuration of the surface.
 17. Amethod according to claim 15 or 16 wherein said agitation is adapted tocreate a vortex in the liquid.
 18. Apparatus for measuring the angle ofa surface of a liquid sample relative to a substrate supporting thesample, comprising a light source for producing a light beam forilluminating the surface at a fixed angle to the substrate and adaptedto illuminate the sample at a predetermined offset from the samplecentre and means for measuring the intensity of the transmitted orreflected light.
 19. Apparatus according to claim 18 wherein thesubstrate comprises a well confining the sample, the light beam beingparallel to the walls of the well and at said predetermined offset fromthe centre of the well.
 20. Apparatus according to claim 17 or 18further comprising means for calculating from the intensity of thetransmitted or reflected light the surface tension of the liquid sample.21. A method of measuring the curvature of a surface substantially ashereinbefore described with reference to and as illustrated in theaccompanying drawings.